The current methods for missing link prediction in social networks focus on using data from overlapping users from two social network sources to recommend links between unconnected users. To improve prediction of the missing link, this paper presents the use of information from non-overlapping users as additional features in training a prediction model using a machine-learning approach. The proposed features are designed to use together with the common features as extra features to help in tuning up for a better classification model. The social network data sources used in this paper are Twitter and Facebook where Twitter is a main data for prediction and Facebook is a supporting data. For evaluations, a comparison using different machine-learning techniques, feature settings, and different network-density level of data source is studied. The experimental results can be concluded that the prediction model using a combination of the proposed features and the common features with Random Forest technique gained the best efficiency using percentage amount of recovering missing links and F1 score. The model of combined features yields higher percentage of recovering link by an average of 23.25% and the F1-measure by an average of 19.80% than the baseline of multi-social network source.
The crossing number of graph is the minimum number of edges crossing in any drawing of in a plane. In this paper we describe a method of finding the bound of 2-page fixed linear crossing number of . We consider a conflict graph of . Then, instead of minimizing the crossing number of , we show that it is equivalent to maximize the weight of a cut of . We formulate the original problem into the MAXCUT problem. We consider a semidefinite relaxation of the MAXCUT problem. An example of a case where is hypercube is explicitly shown to obtain an upper bound. The numerical results confirm the effectiveness of the approximation.
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